Pseudo algebraically closed field

Summary

A field $K$ is pseudo algebraically closed, or PAC, if every absolutely irreducible algebraic variety defined over $K$ has a point with coordinates in $K$. Algebraically closed fields are PAC, but many PAC fields are far from algebraically closed. PAC fields are a central notion of field arithmetic, and their theory links Galois theory with model theory through the absolute Galois group.